Problem 44 - Algebra and Trigonometry Real Mathematics, Real People

Question

Evaluate the trigonometric function of the quadrant angle, if possible. $$\cot \frac{\pi}{2}$$

Step-by-Step Solution

Answer

The value of \( \cot \frac{\pi}{2} \) is undefined.

Step 1: Understand the cotangent function

Cotangent is the reciprocal of the tangent function. In other words, \(\cot \theta = \frac{1}{\tan \theta}\). So we need to determine the value of the tangent of the angle in question first.

Step 2: Evaluate the tangent of \(\frac{\pi}{2}\)

Recall that the tangent function is undefined at \(\frac{\pi}{2}\) (or 90 degrees) because at this angle, the unit circle intersects the y-axis, where the x-coordinate is 0 and the y-coordinate is 1. Hence the tangent (\( \frac{y}{x}\)) will be undefined (as we can't divide by zero).

Step 3: Determine the cotangent of \(\frac{\pi}{2}\)

The cotangent is the reciprocal of the tangent. Therefore, \( \cot \frac{\pi}{2} = \frac{1}{\tan \frac{\pi}{2}}\). But as we found in the previous step, the tangent of \(\frac{\pi}{2}\) is undefined. Hence, the cotangent of \(\frac{\pi}{2}\) is also undefined.